Elizabeth Warren was elected the first female senator from Massachusetts on the strength of her promise to be an advocate for middle-class voters and lunch-bucket Democrats, for sure, but also on the coattails of President Obama and with a boost from her fellow women.

An exit poll from UMass Amherst showed a huge gender gap that broke in her favor on Tuesday. Women voted for Warren 60 percent to 40 percent, while men split 50/50 between the Harvard Law school professor and Senator Scott Brown, the Republican incumbent she sought to unseat.

Furthermore, Warren won 95 percent of the votes from those who supported fellow Democrat Martha Coakley in her unsuccessful 2010 special election campaign against Brown. The senator, by contrast, was able to retain the votes of only 83 percent of those who backed him in that race, the exit poll found.

More impactful: Of the 21 percent surveyed who said they did not vote in that special election, 60 percent voted Tuesday for Warren, while only 40 percent voted for Brown.

Those details put a fine point on a decisive 54 percent-to-46 percent win that validated the Democrats’ belief their candidate would benefit in heavily Democratic Massachusetts from the extra turnout occurring in a presidential election year.

“For every family that has been chipped and squeezed and hammered, we’re going to fight for a level playing field and we’re going to put people back to work,” Warren told jubilant supporters at the Fairmont Copley Plaza Hotel.

“And to all the women across Massachusetts, to all the women across Massachusetts who are working your tails off, you better believe we’re gonna fight for equal pay,” Warren added. “To all of you, this is your night, this is your victory. Yes, all of us.”

Nonetheless, the Democrat toned down her partisanship as she reached out to the supporters of Brown, who took great pride in a Congressional Quarterly voting analysis that found him to be the second-most bipartisan member of the US Senate.

“The message you sent was clear: We need leaders in Washington who are willing to break the partisan gridlock and work regardless of party,” said Warren. “I know I didn’t earn your vote, but I promise, I’m going to work to earn your support.”

For his part, Brown delivered a magnanimous concession speech just blocks away at the Park Plaza Hotel, highlighting the personal charm that has consistently made him the state’s most popular politician in polls.

He also peppered his speech with hints that his political career is far from over, whether it is a campaign for governor in 2014, or another potential Senate candidacy should his senior colleague, Senator John Kerry, be appointed secretary of state by the newly reelected president.

“You’ve got no business in politics unless you respect the judgment of people,” said Brown, who famously claimed “the people’s seat” in 2010. “And if you run for office, you’ve got to be able to take it either way, winning or losing. And I accept the decision of the voters and I have already offered my sincerest congratulations to Senator-elect Warren.”

Brown added: “What matters even more is what we achieved in between these two elections. I kept my promise to you to be that independent voice for Massachusetts, and I have never ever, ever regretted any decision I made for you. You all sent me to Washington to be my own man, and I will return my own man, and I am very very proud, so thank you for that opportunity.”

The still-senator then stepped back and used his bully pulpit for a far larger purpose: aiming to inspire any hard-luck children - like he once was - who might draw the wrong lesson from his defeat.

“We live in the greatest country in the world, and I am so thankful for the opportunities,” he said. “And when it seems that nothing is possible and the odds are stacked against you, let me tell you, and I speak from experience, anything is possible. There are no obstacles you can’t overcome, and defeat is only temporary.”

That line hinted that Brown is likely far from done in the political arena, having run statewide twice and built a national political brand name as a moderate.

That history, his national fund-raising base, as well as his prior work as a state legislator, would make him a natural candidate for governor in 2014. Massachusetts voters have shown a willingness to check the Democratic Legislature with a Republican governor, most recently from 1991 to 2007, from Governor William F. Weld to Governor Mitt Romney.

Brown could also gear up for another Senate campaign, given Tuesday’s results.

Not only was Obama reelected, but Democrats retained their majority in the Senate. Both were necessary preconditions for the president considering tapping Kerry as a replacement for Secretary of State Hillary Rodham Clinton, who has said she will not serve in a second Obama term.

Were the president to do so, Governor Deval Patrick would appoint a temporary successor - most likely a fellow Democrat - and then a special election would have to be held by the end of June to fill the Senate seat permanently.

Brown already has the machinery in place, and the Democrats tapped their best Senate candidate when they recruited Warren to run against the senator.

Yet Kerry’s term will expire in 2014, meaning Brown would have to keep running another two years even if he were successful in winning yet another special election campaign.

During an interview Monday in Beverly, Brown made clear he wouldn’t shy from such a campaign for a lack of effort.

“I love to work,” he said. “I’m a workaholic. I only have one gear, and that’s all-out.”

But after labeling the Senate “dysfunctional” in a concession speech that vacillated between a formal script scrolling across a TelePrompTer to informal shout-outs to audience members, Brown may decide that it’s a better use of his time and political capital to run instead in two years for CEO of the state.

“Let me tell you something: I have left everything in this battle, and I’ll tell you what, I just want to thank you for this opportunity,” he told his crowd of supporters. “And whatever the future holds, I’m a fortunate man to be where I’ve been, and I’m very fortunate ... to return to a place I love more than anything in the world.”